The design of radio frequency power amplifiers for communication applications often involves a trade-off between linearity and efficiency. Typically, power amplifiers (PAs) are most efficient when operated at or near saturation. However, the response of the power amplifier at or near the point of saturation is non-linear. As such, generally speaking, an output response of a power amplifier is non-linear and exhibits memory effects when the power amplifier is operating in the power amplifier's high-efficiency range.
One way to improve the efficiency and overall linearity of a power amplifier is to digitally predistort the input to the power amplifier to compensate for the distortion introduced by the power amplifier. In effect, the input signal is adjusted in anticipation of the distortion to be introduced by the power amplifier such that the output signal of the power amplifier is substantially free of distortion products. Generally, digital predistortion is applied to the input signal at baseband frequencies, i.e., before the input signal is up-converted to a desired radio frequency.
To illustrate, a power amplifier may exhibit first and third order effects characterized by a polynomial function of the input that may be written for third order non-linearities as:y=fNL-IM 3(x)=a1x+a3x3  (1)where x is the input signal and the coefficient a3 is much smaller than a1. The function fNL-1M3 is the response of the power amplifier to the input x and the subscript NL-IM3 denotes non-linearity up to order three. To compensate for the distortion introduced by the power amplifier, a predistorter may have a response that is a polynomial function of the input:z=fPD-IM 3(x)=b1x+b3x3  (2)where again x is the input signal and the function fPD-IM3 is the response of the predistorter to the input x.
Substituting Equation (2) into Equation (1) leads to:y=fNL-IM 3(fPD-IM 3(x))=a1b1x+(a1b3+a3b13)x3+O(x5)  (3)where O(x5) are terms of fifth-order or higher. By appropriate selection of the coefficients b1 and b3, the third order term may be removed at the expense of creating higher order terms of significantly smaller magnitude. The solution to achieve this is given by:
                              b          3                =                                                            -                                  a                  3                                            ⁢                              b                1                3                                                    a              1                                .                                    (        4        )            Without loss of generality, assuming that a1=b1=1, then the solution to compensate for third-order non-linearities is:b3=−a3.  (5)This simple illustration is for third-order non-linearities. For higher order non-linearities (e.g., fifth-order non-linearities), the same approach may be taken to cancel the higher-order terms.
FIG. 1 illustrates a conventional system 10 that implements this digital predistortion approach to compensate for non-linearities of a power amplifier 12. A baseband (BB) source 14 outputs a baseband signal, which is up-sampled by up-sampling circuitry 16 in provision for bandwidth expansion that occurs inside a predistorter (PD) 18. The predistorter 18 predistorts the up-sampled baseband input signal to provide a predistorted baseband input signal. The predistortion, or non-linearities, introduced by the predistorter 18 compensates for the non-linearities of the power amplifier 12. The predistorted baseband signal is then upconverted to a desired carrier frequency (ωC) and then quadrature modulated by an upconverter 20 and quadrature modulator 22, respectively. The upconverted and quadrature modulated predistorted input signal is then converted from digital to analog by a digital-to-analog converter (DAC) 24 to thereby provide a power amplifier input signal. The power amplifier input signal is then amplified by the power amplifier 12. Again, the predistortion introduced by the predistorter 18 compensates, or effectively cancels, the distortion caused by non-linearities of the power amplifier 12.
The power amplifier output signal is fed back into an observation receiver 26. As illustrated, the observation receiver 26 includes a wideband filter 30, an attenuator 32, downconversion and demodulation circuitry 34, and an analog-to-digital converter (ADC) 36 arranged as shown. The output of the observation receiver 26 is referred to herein as an observation signal (SO). An adaptor 28 then adaptively configures the predistorter 18 based on a comparison of time-aligned as well as gain and phase adjusted versions of the observation signal (SO) and a reference signal (SR), which in this case is the up-sampled input signal input into the predistorter 18. Specifically, the adaptor 28 configures the coefficients of the predistorter 18 based on the comparison of the time-aligned as well as gain and phase adjusted versions of the observation signal (SO) and the reference signal (SR). Notably, together, the predistorter 18, the observation receiver 26, and the adaptor 28 are referred to herein as a digital predistortion (DPD) system 38 whereas the observation receiver 26 and the adaptor 28 are referred to herein as an adaptation subsystem 40 of the digital predistortion system 38.
One issue with the digital predistortion system 38 is that the non-linearities of the power amplifier 12 result in bandwidth expansion which in turn results in increased sampling rate requirements for the predistorter 18 and the adaptor 28. More specifically, as illustrated in FIG. 2, the reference signal (SR) has a bandwidth (B). In contrast, as a result of both predistortion and the non-linearities of the power amplifier 12, the observation signal (SO) suffers from bandwidth expansion. The bandwidth expansion is equal to NMAX—ORDER times B, where NMAX—ORDER is the maximum order of non-linearities of the power amplifier 12 for which the digital pre-distortion subsystem 38 is designed to compensate. Specifically, as illustrated in FIG. 3, fifth-order non-linearities, for example, cause the spectrum of the observation signal (SO) to occupy five times the bandwidth (B) of the reference signal (SR). Thus, when compensating for up to fifth-order non-linearities of the power amplifier 12, the digital predistortion system 38, and in particular the adaptation subsystem 40, is designed to support a bandwidth of five times the bandwidth (B) of the reference signal (SR) (i.e., 5×B). In other words, the wideband filter 30 is designed such that a bandwidth of the pass-band of the wideband filter 30 is five times the bandwidth (B) of the reference signal (SR). When compensating for up to fifth-order non-linearities, the sampling rate of the adaptor 28 is therefore greater than five times the bandwidth (B) of the reference signal (SR).
As the need for bandwidth increases in wireless communications systems (e.g., cellular communications networks), the digital predistortion system 38, and in particular the adaptation subsystem 40, must support a much larger bandwidth. These very large bandwidths are challenging for hardware implementations. Further, even if hardware can be designed to support these wide bandwidths, the resulting hardware requires a significant amount of resources and power. As such, there is a need for an adaptation subsystem for a digital predistortion system that minimizes, or substantially reduces, resource and/or power requirements.